As discussed above, we need the \(\tilde{V}\)  and \(\tilde{m}_{i}\)  to obtain the probabilities. One can get the values of PMNS matrix, in the presence of DM, from the eigenvector-eigenvalue identity[1]}
\({\tilde{V}_{\alpha _i}}^{2} = \frac{(\lambda _{i}-\xi _{\alpha })(\lambda _{i}-\zeta _{\alpha })}{(\lambda _{i}-\lambda _{j})(\lambda _{i}-\lambda _{k})},\) 
